sin4f 



Scliuherfs investigation of Eepler^s Prohlem. 



I 



sin 4^+2e(sin 5«— sin 3iA.)+e^{5 sin 6^4—4 sin 4^+sin 2^*) 



IS 



"^ 22^^''^ •^'"'''"~^*^'*^*"^'^+^ ^•^^"^^s^'^ '^) +|-(2'^-si" 8.«-3 ^sin 6^6+23 .S sia4ict-sln 2^^ 

 "^ 2^33^^ ^•^'^^^"^•^^•^^° 7'Ac+2.5«.sin5itt-2.3*.5.siii 3itt+2.3.sia^c) 



"^'a^ijiTs C^^'S"^ 1 0^-^21 i.S.sin 8^+36.5.sin 6ft— 2',5.sin 4ft+2*.sin 2/*) 



8 



^ 



sm 5£=sin 5^6+ — e(sm 6A«.-sin 4^*) + -^(J sin 7|a— lO.sin 5itt+3.sin Siu.) 



2 



23 



S"'* 



'^ 2^3 (^^''•^^'^ 8/*— 33.sin 6At+22.3.sin 4^— sin 2,«) 



5e 



+ ^7^^ (Ss.sin 9 1*-~9.'^ ,7 ^ ,%m 7^4+2.3.5'. sin 5/«^25.33.sin S.tt+sin (jC\ 



+ 



5es 





-(53.sln 10m— ss.sin 8.t6+2.3*.sin 6/* — 25.sin4iM.+sin S^c) 



+ 2i"r;7 (1 l^sin 11^2.31 i.sin O/tt + 3. 5.7* .sin 7A*-22.5s.sin 5At+3«.5.sin 3.u-5 sin /*) 



+ 5 2 .^CQ^'S°.sin I2^5^7.sin 10/«+2i2.3.7.sin8A4-3«.o.7.sin6;tt+2«.5.7.sin4jw-22.5^iu2M): 



in 6 



sio 6^+3^ (sin T^t — sin 5At)+5e2(2 sin 8jtt— 3 sin 6^+ sin 4^^) 



+ 



3^3 



2 



3 



C33.sin 9jte— 72.sin7^+52.sin 5^^^ 



3 



sin 3^) 





2s.sin 8iie+2.3'*.sin Gjtt — 2* .sin 4/t-f sin 2^-) 



+ 27~5 C' I'^.sin lift— 38.5.sin9/*+2,5.7'*.sin 7^— 2.5*.sin 5.**+3*,5 sin Sjm. — gin/i) 

 + —:: (2'».3*sin 12^*— a'.sin 10f4+29.5.sin 8/*— 2.3'».5.sin 6M+2*.5.siu 4^— sin 2^): 



7 



7t 



sin 7«=sia 7ft+ ^f(sin 8^— sin 6/tt)+ ^(32.9in 9/*— 2,7.sin7/»+5 si'n 5^) 



2 



23 



7e^ 



+ ?T-; ( J^.sin 10.«.— S^.S.sin 8;«.4-3^.sin G^it— S^.sin 4/*) 



^ »o 



3 



